... or does wp_title() already handle the various contexts in your blog?

This could clarify for me how I can achieve a reusable index.php file without having all the conditional statements inside it to handle the different title formats in the given context (page, single, posts, search, archive, date, etc...)

Also,

Could a specific post or page have a special custom formatting without breaking the rest of the use-cases? (If this needs to be in a separate question, please let me know - it's closely tied to this question so I figured I'd merge it in here for now).

In case it isn't obvious, these filter callbacks belong in functions.php.

EDIT

Missed this:

Could a specific post or page have a special custom formatting without breaking the rest of the use-cases?

It is entirely possible. In fact, that's how most SEO Plugins work.

Here's the thing about using the wp_title filter to control wp_title() output: you've built in the ability to play nicely with SEO Plugins and anything else that attempts to modify wp_title() content, with no additional code changes required.

Thanks Chip! I was just about to ask before I read the whole thing whether or not the filter-hooks goes into functions.php - You sir provide the greatest answers I've seen so far! :)
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bigpNov 1 '11 at 15:58

Does adding filters override the wp_title() functionality? Or does it add to existing filters of it?
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bigpNov 1 '11 at 15:59

"Does adding filters override the wp_title() functionality? Or does it add to existing filters of it?" - it depends on what you return. You can completely override it, or just append content.
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Chip BennettNov 1 '11 at 16:26

Missed the second part of your question; it's now been added as an edit to my answer.
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Chip BennettNov 1 '11 at 19:01

Correct me if I am wrong, but I do not think that there is a "clean" way of doing titles without using conditionals. As far as the per-page title goes, you could create a custom meta field and check for the presence of it when you output your title.